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The key to shale gas exploration is the characterization of gas migration under the combination of multiple factors. To address the long-standing energy challenge of rapidly and accurately quantifying the behavior of natural fractures and matrix pores in shale at an engineering scale in interaction with gas migration. This study proposes an interdisciplinary model for shale gas extraction by adopting fractal theory. Five innovative microstructural parameters are developed to characterize the size and scale of natural matrix pores/fractures in shale, so as to investigate the contributions of fractal distributed pores and fractal power-law distributed fractures to shale gas extraction. The present results of the proposed model are consistent with the exploitation state of the UK Bowland Shale #114 well. The evolution of the shale microstructure will lead to changes in gas migration behavior throughout the reservoir and in turn affect shale stress, temperature and gas adsorption–desorption effect, and finally have a significant impact on permeability. It is found that in the present analysis of the entire Bowland Shale, the overall permeability changes by 10.8% with the evolution of fractal distributed pores and by 41.3% with the evolution of fractal power-law fractures. This work provides a new approach for rapidly exploring the behavior of shale fractures and matrix pores at engineering scales. This work also offers a new and practical baseline for shale gas extraction assessment and fossil energy management. [ABSTRACT FROM AUTHOR]

Summary: The long-term flow recession of many springs can be approximated by an exponential function. However, the early recession often exhibits a different behaviour. The exponential recession function represents a long-term approximation of analytical solutions of the flow equation of fissured matrix blocks draining toward a fixed-head boundary. Thus, early deviations from the exponential behaviour potentially originate from the inappropriateness of this approximation at short times. We therefore examine the properties of the exact analytical solutions and make comparisons with field data. If hydraulic heads are initially constant within the matrix blocks the flow recession exhibits a power-law decrease at short times. Both from steady-state initial conditions and after finite recharge pulses the early flow recession follows a power law, too, if discharge is appropriately shifted and rescaled. If the catchment is composed of multiple blocks drained by highly conductive conduits the recession behaviour of the spring is identical to that of the individual blocks if the blocks are of the same size. The recession curves of the published hydrograph of Cheddar spring (Great Britain) are found to be in good agreement with this model if reasonable initial conditions are assumed. A brief look at recession curves from other springs suggests that the model might be applicable to most of them, too. The model also provides satisfactory fits to the flow recession of the Gallusquelle (Germany). However, the observed power-law exponent differs from that predicted by the analytical model. A consistent interpretation of the shape of several recession curves from this spring is provided by a more general fractal approach, which assumes that the catchment is composed of blocks of strongly different sizes. [Copyright &y& Elsevier]

1 The distribution patterns of 391 rare and scarce British plants (species recorded in 100 or fewer 10 × 10 km squares) were characterized by their distributional area (area of occupancy at 1-km scale: AOO1) and levels of aggregation (as reflected in fractal dimensions measured across two scales: D1−10 and D10−100). 2 Eighteen plant traits were tested for relationships to AOO, and to fractal dimension while controlling for AOO. These included both directly heritable traits (e.g. life-form) and emergent properties that are, at most, indirectly heritable (e.g. typical local density). The latter set included an index of net distributional change and an index of range dynamism. 3 Only two traits, habitat preference and local abundance, were significantly related to AOO1, but about half were associated with fractal dimension. 4 Relatively aggregated fine-scale distributions (high D1−10) were related to high local abundance, lack of specialized, long-distance dispersal mechanisms, habitat preference and an increasing range size with relatively few local extinctions (i.e. a positive index of change with low dynamism). 5 Relatively aggregated coarse-scale distributions (high D10−100) were related to the use of insect pollinators, obligate outcrossing, habitat preference and relatively stable ranges (low dynamism). 6 Multivariate analyses of subsets of conceptually related variables showed that few variables interacted to affect distributional variables. 7 A highly significant negative relationship between dynamism and fractal dimension appears to be driven primarily by high rates of local extinction, leading to relatively scattered, diffuse range structures. Furthermore, it suggests that recent population trends may be inferred from snapshots of contemporary distribution patterns. 8 The role and interpretation of phylogenetically informed analyses in studies such as this are debatable. However, we found similar relationships in both phylogenetically informed and conventional analyses for all variables except pollination vector (a strongly conserved trait). 9 The spatial pattern of plant species distributions is associated with a range of ecological traits, particularly those describing past changes in distribution. The analysis of distribution patterns therefore has the potential to inform future conservation effort. [ABSTRACT FROM AUTHOR]